DLR.de • Chart 1
Validation of the
Driving by Visual Angle
car following model
David Käthner & Diana Kuhl
Institute of Transportation Systems
DLR Braunschweig
DLR.de • Chart 2
Why modelling car following?
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Examples of models
Box-and-Arrow
Carsten (2007)
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Examples of models
Cognitive architecture, production rules
(p decide‐lc‐lane1
=goal>
isa drive
stage decide‐lc
task lk
lane lane1
v =v
fkind car
fthw =thw
!eval! (< =thw *thw‐pass*)
==>
=subgoal>
isa check‐lc
lane lane1
v =v
result =result
!push! =subgoal
=goal>
stage =result)
(Salvucci, e.g. 2005)
DLR.de • Chart 5
Examples of models
Psychophysical controller for car following behavior
Anderson and Sauer (2007)
DLR.de • Chart 6
Some properties of driver models
Properties
DLR.de • Chart 7
Some properties of driver models
qualitative
(verbal)
Formalization
quantitativ
(computational)
Properties
DLR.de • Chart 8
Some properties of driver models
qualitative
(verbal)
Formalization
quantitativ
(computational)
Properties
micro
Scope
macro
DLR.de • Chart 9
Some properties of driver models
qualitative
(verbal)
Formalization
machine
learning
quantitativ
(computational)
Properties
rules
micro
approach
controller
(open / closed
loop)
Scope
macro
DLR.de • Chart 10
Some properties of driver models
qualitative
(verbal)
descriptive
explicative
machine
learning
Psychological
Formalization
claim
quantitativ
(computational)
Properties
micro
approach
rules
controller
(open / closed
loop)
Scope
macro
DLR.de • Chart 11
Some properties of driver models
cognition
Purpose
Formalization
evaluation
descriptive
explicative
machine
learning
rules
controller
(open / closed loop)
qualitative
(verbal)
Psychological
claim
quantitativ
(computational)
Properties
micro
approach
Scope
macro
DLR.de • Chart 12
Some properties of driver models
cognition
Purpose
Formalization
evaluation
descriptive
explicative
machine
learning
rules
controller
(open / closed loop)
qualitative
(verbal)
Psychological
claim
quantitativ
(computational)
Properties
micro
approach
Scope
macro
DLR.de • Chart 13
Some properties of driver models
cognition
Purpose
Formalization
evaluation
descriptive
explicative
machine
learning
rules
controller
(open / closed loop)
qualitative
(verbal)
Psychological
claim
quantitativ
(computational)
Properties
micro
approach
Scope
macro
DLR.de • Chart 14
Why modelling car following?
basic driving task
• essential for higher cognition driver models
• comparatively easy modelling of a driving task
extremely useful for design of assistance systems
lacking so far
• good data on individual car-following behavior
• systematic evaluation of models on this data
we contribute to close that gap
• data for individual drivers
• from real traffic with instrumented vehicle
• systematic variation of road type (city, highway, country)
DLR.de • Chart 15
Basic driving tasks
from Hakuli et al. (n.d.) according to Donges (1982)
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Control level of driving
trajectory /
maneuver level
anticipatory
open loop
road and
traffic
situation
task irrelevant
steering
behavior
steering angle
vehicle
dynamics
compensatory
closed loop
stabilizing /
control level
output feeds back
adapted from Donges (1978)
DLR.de • Chart 17
A very simple car following model
with
accelerationattime ,
velocityleadvehicleonetimestepago,
velocityfollowingvehicleonetimestepago,
freeparameter
Pipes (1953)
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A very simple car following model
basic algorithm
1.
2.
3.
4.
5.
6.
7.
choose a start parameter for s
take values for leading vehicle from data
take first value for following vehicle from data
compute prediction for the next time step by using the predicted a
do so until the end of the vector
compute error metric
test next parameter, until the error metric is at a minimum
DLR.de • Chart 19
A very simple car following model
DLR.de • Chart 20
A very simple car following model
DLR.de • Chart 21
The Gipps model
∙τ
with
∙ 2∙
∙τ
Gipps (1981)
mostseverebrakingofthedriver,
estimatedbrakingoftheleadingvehicle,
safetydistance,
velocityofleadingvehicleattimet,
τ apparentreactiontime,aconstantforallvehicles,
velocityleadvehicleonetimestepago,
velocity following vehicleone timestep ago
DLR.de • Chart 22
The Helly model
with
∙
,
safetydistance,
velocityleadvehicleonetimestepago,
velocityfollowingvehicleonetimestepago,
weightfactor,
timestep
Helly (1959)
DLR.de • Chart 23
The Driving-by-Visual-Angle model
with
2∙
and
visualangle,
desiredvisualangle,
w widthofleadcar,
THW timegap,
velocityleadcar
∙
DLR.de • Chart 24
The Driving-by-Visual-Angle model
α
width
distance
α
2 ∗ atan
2∗
Helly‘s model vs. DVA
Helly
DVA
DLR.de • Chart 26
Validation methods
driving simulator: often sinusoidal speed profiles
• disadvantage: might be too artificial
real driving data: cameras, induction loops etc.
• disadvantage: dirty data, absolutely no control over situation
DLR.de • Chart 27
Methods
12 participants over 8 weeks, on
Sundays / public holidays only
road types:
• highway
• city (straight and curved road)
• country
70 km, 2 hours drive
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Methods
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Predictions unoptimized
DVA is unstable!
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Predictions unoptimized
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Predictions unoptimized
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Results constrained, distance
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Results constrained, distance
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Results unconstrained, speed
DLR.de • Chart 35
Results unconstrained, speed
DLR.de • Chart 36
Discussion
DVA does not hold its promises
• a few psychophysical additions doesn’t make it psychologically
plausible!
• unstable controller?
degree of psychology in car following controllers
• non-trivial question
• depends a lot on handling of parameters
interaction of parameters and optimization algorithm
• some algorithms are more sensitive to starting parameters than others
DLR.de • Chart 37
Outlook and Lessons Learned
systematic evaluation
• more models
• different driving simulators
• possibly new data collection in the field with better sensors
parameter
• other optimization algorithms
• windowing
• maximum likelihood methods
• bootstrapping
• grid search
more computational power / less precision
• more efficient code
• cluster
• less optimized parameters
DLR.de • Chart 38
Literature
Andersen, George J.; Sauer, C. W. (2007): Optical Information for Car Following: The Driving by
Visual Angle (DVA) Model. In: Human Factors 49 (5), S. 878–896. DOI: 10.1518/001872007X230235.
Carsten, Oliver (2007): From Driver Models To Modelling The Driver: What Do We Really Need
To Know About The Driver. In: Pietro Carlo Cacciabue (Hg.): Modelling Driver Behavior In Automotive
Environments. Critical Issues in Driver Interactions with Intelligen Transport Systems. London:
Springer, S. 105–120.
Donges, Edmund (1978): Ein regelungstechnisches Zwei-Ebenen-Modell des menschlichen
Lenkverhaltens im Kraftfahrzeug. In: Zeitschrift für Verkehrssicherheit 24 (3), S. 98–112.
Gipps, P.G (1981): A behavioural car-following model for computer simulation. In: Transportation
Research Part B: Methodological 15 (2), S. 105–111. DOI: 10.1016/0191-2615(81)90037-0.
Hakuli, Stephan; Schreiber, Michael; Winner, Hermann (2009): Entwicklung eines
Methodenkatalogs für manöverbasiertes Fahren nach dem Conduct-by-Wire-Prinzip. Ein
Fahrerassistenzkonzept auf Bahnführungsebene. Automobiltechnisches Kolloquium, 2009.
Helly, W. (1959). Simulation of Bottlenecks in Single Lane Tracffic Flow. In Proceedings of the Symposium on Theory of Tracffic Flow., Research Laboratories, General Motors (pp. 207±238). New York: Elsevier .
Salvucci, Dario D. (2005): Modeling Driver Behavior in a Cognitive Architecture. In: Human
Factors.
Soria, Irene; Elefteriadou, Lily; Kondyli, Alexandra (2014): Assessment of car-following models by
driver type and under different traffic, weather conditions using data from an instrumented vehicle. In:
Simulation Modelling Practice and Theory 40, S. 208–220. DOI: 10.1016/j.simpat.2013.10.002.